failed to resolve com.android.support:appcompat-v7:22 and com.android.support:recyclerview-v7:21.1.2

These are the correct version that you can add in your build.gradle according to the API needs.

API 24:

implementation 'com.android.support:appcompat-v7:24.2.1'
implementation 'com.android.support:recyclerview-v7:24.2.1'

API 25:

implementation 'com.android.support:appcompat-v7:25.4.0'
implementation 'com.android.support:recyclerview-v7:25.4.0'

API 26:

implementation 'com.android.support:appcompat-v7:26.1.0'
implementation 'com.android.support:recyclerview-v7:26.1.0'

API 27:

implementation 'com.android.support:appcompat-v7:27.1.1'
implementation 'com.android.support:recyclerview-v7:27.1.1'

In order to make that working I had to set:

compile ("com.android.support:support-v4:22.2.0")
compile ("com.android.support:appcompat-v7:22.2.0")
compile ("com.android.support:support-annotations:22.2.0")
compile ("com.android.support:recyclerview-v7:22.2.0")
compile ("com.android.support:design:22.2.0")

compile ("com.android.support:design:22.2.0")

Documentation states something different (docs):

com.android.support:support-design:22.0.0